First, draw the chart below with SIN TAN SEC on left,
CO-functions on right, and 1 in the middle.
+---------------+
| |
| SIN-----COS |
| \ / |
| \ / |
| \ / |
| TAN--1--COT |
| | / \ | |
| | / \ | |
| |/ \| |
| SEC CSC |
| |
+---------------+
Using this chart (I just look at it in my head) you can remember the following things:
Across the 1:
1/SIN = CSC or 1/CSC = SIN
1/TAN = COT or 1/COT = TAN
1/SEC = COS or 1/COS = SEC
Down any triangle:
SIN2 + COS2 = 1
TAN2 + 1 = SEC2
1 + COT2 = CSC2
Up any triangle:
SEC2-1 = TAN2 or 1-TAN2 = SEC2
CSC2-1 = COT2 or CSC2-COT2 = 1
1-SIN2 = COS2 or 1-COS2 = SIN2
A function and its two nearest CLOCKWISE or COUNTERCLOCKWISE neighbors
around any edge of the square:
(listed starting at TAN going clockwise)
TAN = SIN/COS
SIN = COS/COT
COS = COT/CSC
CSC = SEC/TAN
SEC = TAN/SIN
(listed starting at TAN going counter-clockwise)
TAN = SEC/CSC
SEC = CSC/COT
CSC = COT/COS
COS = SIN/TAN
SIN = TAN/SEC
A function and its two neighbors around any edge of the square:
(listed starting at TAN going clockwise)
TAN = SIN*SEC
SIN = COS*TAN
COS = COT*SIN
CSC = COT*SEC
SEC = TAN*CSC
Don't forget to put in the arguments in each of the identities above!!